1. Field of the Invention
The invention relates to communication systems that use multiple carriers to improve the bandwidth efficiency of the communication systems, where the carriers are locally orthogonal (but not necessarily globally orthogonal) according to a desired transform.
2. Description of the Related Art
Many communication channels, such as, for example, Radio Frequency (RF) channels, power line channels, and the like, often present a hostile transmission environment for the desired communication signals. These hostile channels can produce a variety of interference mechanisms, including multipath interference, amplitude fading, phase shifts, noise, etc.
In an ideal communication channel, the received signal would consist of only a single direct-path received signal, which would be a perfect reconstruction of the transmitted signal. However in a real channel, the signal is modified during transmission in the channel. The received signal typically comprises a combination of attenuated, reflected, refracted, and diffracted replicas of the transmitted signal. Moreover, the channel typically adds noise to the signal and, in some environments, can cause a shift in the carrier frequency. Understanding these effects on the signal is important because the performance of a communication system is dependent on the channel characteristics.
Attenuation is a drop in the received signal strength. Attenuation can be caused by the transmission path length, obstructions in the signal path, loss in the signal path, and multipath effects. In many systems, especially radio-based systems, the signal from the transmitter may be reflected from discontinuities such as hills, buildings, or vehicles. This gives rise to multiple transmission paths from the transmitter to the receiver. In communication systems that use a guide, such as a waveguide, coaxial cable, fiber-optic cable, twisted pair cable, power line, etc, multipath effects can occur from discontinuities due to impedance mismatches on the cable, connectors, junctions, etc.
As a result, the channel spectral response is typically not flat or uniform. The spectral response has dips or peaks in the response due to loss in the channel and due to reflections from discontinuities. Reflections from near-by discontinuities can lead to multipath signals of similar signal power as the direct signal. This can cause deep nulls in the received signal power due to destructive interference. For narrow-band channels, if the null in the frequency response occurs at the transmission frequency, then the entire signal can be lost. This can be partially overcome in various ways. For example, by transmitting a wide-bandwidth signal (e.g. spread-spectrum), any dips in the spectrum only result in a small loss of signal power. Another method is to split the transmission up into many small bandwidth carriers, as is done in FDM/OFDM systems. The original signal is spread over a wide bandwidth, thus any nulls in the spectrum are unlikely to occur at all of the carrier frequencies. This will result in only some of the carriers being lost, rather than the entire signal. The information in the lost carriers can be recovered by various techniques, including, for example, forward error correction, retransmission on good carriers, etc.
The received signal from a transmitter typically includes a direct signal, plus reflections from various discontinuities in the channel. The reflected signals often arrive at a later time than the direct signal because of the extra path length to the discontinuity, giving rise to a slightly different arrival time of the transmitted pulse, thus spreading the received energy. Delay spread is the time spread between the arrival of the first and last multipath signal seen by the receiver.
In a digital system, the delay spread can lead to inter-symbol interference. This is due to the delayed multipath signal overlapping with the following symbols. This can cause significant errors in high bit rate systems, especially when using time division multiplexing (TDMA). As the transmitted bit rate is increased, the amount of inter-symbol interference typically also increases. The effect usually starts to become very significant when the delay spread is greater than ˜50% of the bit time.
For digital communication systems operating at relatively high data rates, that is data rates that approach the Shannon limit for the channel, data bits are often collected into groups and transmitted as symbols. Each received symbol represents one or more bits. One technique often used to improve communication over a hostile channel is to extend of the duration of the symbols by increasing the dimension of the symbol alphabet. In spread-spectrum systems the symbols have a wide spectrum and a narrow auto-correlation function. Unfortunately, the spectral efficiency of this type of system is relatively low and therefore unsuitable for systems where high spectral efficiency is desired.
Another approach for dealing with a hostile channel includes separating the information to be transmitted into a large number of elementary sub-channels, where each sub-channel carries a relatively low bit-rate. This technique, known as Frequency Division Multiplexing (FDM), transforms a highly selective wide-band channel into a large number of non-selective narrow-band channels that are frequency-multiplexed. With FDM there remains the problem of fading. That is, the amplitude of each of the sub-channels follows a Rayleigh law, or a Rice-Nakagami law. The use of a coding system adapted to the fading nature of the channel permits the performance to be considerably improved.
In a conventional (non-orthogonal) FDM system, the many carriers are spaced in such a way that the signals can be received using conventional filters and demodulators. In such receivers, guard bands are introduced between the different carriers. The guard bands represent wasted spectrum and produce a lowering of the spectral efficiency.
In FDMA each user (or each packet in a packet-based system) is typically allocated a single channel, which is used to transmit all the user information. For example, the bandwidth of each channel is typically 10 kHz–30 kHz for voice communications. However, the minimum required bandwidth for speech is only 3 kHz. The allocated bandwidth is made wider than the minimum amount required to prevent channels from interfering with one another. This extra bandwidth is to allow for signals from neighboring channels to be filtered out, and to allow for any drift in the center frequency of the transmitter or receiver. In a typical system up to 50% of the total spectrum is wasted due to the extra spacing between channels. This problem becomes worse as the channel bandwidth becomes narrower and the frequency band increases.
Orthogonal Frequency Division Multiplexing (OFDM) is a special form of FDM wherein the various carriers are made orthogonal to each other. Orthogonal carriers do not interfere with each other, and thus the carriers can be closely spaced. OFDM is similar to FDM in that the multiple user access is achieved by subdividing the available bandwidth into multiple channels that are then allocated to users (or packets). However, OFDM uses the spectrum much more efficiently by spacing the channels much closer together.
Coded Orthogonal Frequency Division Multiplexing (COFDM) is the same as OFDM except that forward error correction is applied to the signal before transmission. This is to overcome errors in the transmission due to lost carriers from frequency selective fading, channel noise and other propagation effects. For this discussion the terms OFDM and COFDM are used interchangeably since forward error correction bits can be added to the data in an OFDM system.
With OFDM, the maximum signaling rate for the given channel (Nyquist rate) can be approached without the use of sharp cutoff filters, thereby facilitating high-speed data transmission. The OFDM system is less sensitive to interference from wide-band impulse noise than time division multiplexing (TDM) systems.
Conceptually, in an FDM system, the carriers are generated by a bank of sinusoidal generators, and then modulated by a bank of modulators. The sinusoidal carriers are more generally referred to as basis functions.
The received carriers are demodulated by a bank of demodulators. For a large number of sub-channels, the arrays of sinusoidal generators, modulators, and demodulators can become unreasonably expensive and complex. Fortunately, an OFDM data signal is effectively the Fourier transform of the original data train, and the bank of coherent demodulators is effectively an inverse Fourier transform generator. A digital OFDM modem can be built around a computer performing Fourier transforms and inverse Fourier transforms.
The orthogonality of the carriers means that each carrier has an integer number of cycles over a basis function period. The spectrum of each carrier has a null at the center frequency of each of the other carriers in the system. Orthogonality also means there is no interference between the carriers, allowing the carriers to be spaced more closely than in FDM systems. This largely overcomes the spectral inefficiencies found in non-orthogonal FDMA systems.
Each channel in an OFDM signal has a relatively narrow bandwidth, thus the resulting symbol rate on each channel is lower than the symbol rate that could be obtained using TDMA on the same medium. This results in the signal having a high tolerance to multipath delay spread, as the delay spread must be very long to cause significant inter-symbol interference. Also an OFDM system is spectrally much more efficient than the traditional FDMA type system where no spectral overlap is allowed.
To generate OFDM, the relationship between the carriers is controlled to maintain the orthogonality of the carriers. Each carrier to be produced is assigned some data to transmit. The required amplitude and phase of each carrier is then calculated based on the desired modulation scheme (e.g., differential BPSK, QPSK, QAM, etc.). The required spectrum is then converted back to its equivalent time-domain signal using an Inverse Fourier Transform. In most applications, an Inverse Fast Fourier Transform (IFFT) is used. The IFFT performs the transformation very efficiently, and provides a simple way of ensuring the carrier signals are orthogonal.
The Fast Fourier Transform (FFT) transforms a cyclic time domain signal into its equivalent frequency spectrum. This is done by finding the equivalent waveform, generated by a sum of orthogonal sinusoidal components. The amplitude and phase of the sinusoidal components represent the frequency spectrum of the time domain signal. The IFFT performs the reverse process, transforming a spectrum (amplitude and phase of each component) into a time domain signal. An IFFT converts a number of complex data points into the time domain signal of the same number of points. Each data point in the frequency spectrum used for an FFT or IFFT is called a bin.
The orthogonal carriers for the OFDM signal can be generated by setting the amplitude and phase of each bin, then performing the IFFT. Since each bin of an IFFT corresponds to the amplitude and phase of a set of orthogonal sinusoids, the FFT, being the reverse process, guarantees that the carriers are orthogonal.
One of the advantages of OFDM transmissions is robustness against multipath delay spread. This is achieved by having a long symbol period, which reduces the inter-symbol interference. The level of robustness can be increased even more by the addition of a guard period between transmitted symbols. The guard period allows time for multipath signals from the previous symbol to die away before the information from the current symbol is gathered. One type of guard period is a cyclic extension of the symbol. Using a mirror in time of the end of the symbol waveform, and placing this mirror image at the start of the symbol, effectively extends the length of the symbol while maintaining the orthogonality of the waveform. Using this cyclic extended symbol, the samples required for performing the FFT (to decode the symbol) can be taken anywhere over the length of the symbol. This provides multipath immunity as well as symbol time synchronization tolerance.
As long as the multipath delay echoes stay within the guard period duration, there is, strictly speaking, no limitation regarding the signal level of the echoes. The echoes can even exceed the signal level of the direct path. The signal energy from all paths just add at the input to the receiver, and since the FFT is energy conservative, the whole available power feeds the decoder. If the delay spread is longer than the guard interval, then they begin to cause inter-symbol interference. Fortunately, longer delay spreads usually correspond to reflections from distant discontinuities, and these reflections tend to arrive at the receiver with a relatively small amplitude (thus causing relatively little interference). Inter-symbol interference occurs when spectrum of a symbol on one sub-channel interferes with the spectrum of a subsequent or prior symbol on the same sub-channel. Inter-carrier interference occurs when the spectrum of a symbol on one channel interferes with the spectrum of a symbol on a different channel
Unfortunately, the need for a guard period reduces the symbol rate that can be transmitted on the channel. A reduced symbol rate corresponds to a reduced data rate. Thus, it is desirable to reduce the length of the guard period. The length of the guard period is driven by two factors. First, the guard period must be long enough to reduce inter-symbol interference on each channel. Second, the guard period must be long enough to cover all channel-to-channel delay spreads. To understand this second requirement, it is observed that the FFT and IFFT operations used in conventional OFDM systems are block operations that are applied to all channels simultaneously. Thus, in a conventional OFDM system, the guard period must be long enough to provide enough delay spread across all channels, even though there is typically no inter-channel multipath effects. This means that the guard period on a conventional OFDM system can significantly reduce the overall system data rate. The length of the guard band is adversely affected by the delay spread across the channels, because the guard band must be long enough to deal with a worst-case delay-spread across all of the channels. In some environments, especially where the channel-to-channel delay spread is very large, the length of the guard band can become prohibitively long and can significantly reduce throughput.